{"title":"Failure and damage evaluation of thermal barrier coatings under thermal cyclic environments: multi-physics modeling","authors":"Jinrong Yan, Kuiying Chen, Xin Wang","doi":"10.1007/s10704-025-00874-y","DOIUrl":"10.1007/s10704-025-00874-y","url":null,"abstract":"<div><p>Under high-temperature adverse environments, the premature failure of air plasma spray thermal barrier coatings (APS-TBCs) is a preliminary phenomenon that can significantly limit the application of TBCs in gas turbine engines. The delamination failure of TBCs typically occurs at the interfaces between the topcoat and bond coat due to thermal mismatch stress and thermal gradient, resulting in crack propagation and final spallation failure of the coating. This paper undertakes a study of the delamination of TBCs using multi-physics methodologies. Heat transfer was cyclically implemented into the TBC model, resulting in a thermal gradient, to simulate the in-service operation of the TBC system. A variational-based sintering model for a topcoat of TBCs is incorporated into the simulation. The high-temperature creep model of the topcoat, thermal growth oxide (TGO) and bond coat is included. The stress field across the TBCs was calculated during the thermal cycles, with the location of high-stress concentration selected as the potential crack initiation site. Phase field damage modelling was conducted to study crack propagation, initially located at the high-tensile stress off-peak interface. Results indicate that at the off-peak interface, the crack propagates rapidly in the top right direction during the first few cycles, then stops propagating as the TGO thickens, because the location of the maximum principal stress is moved away from the interface. Since the accumulated stress at the crack tip at the end of cycles, cracks have the potential to propagate with a prolonged thermal cycle service.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10704-025-00874-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A novel phase-field damage model coupled with Timoshenko beam kinematics to simulate localized fracture in brittle architected lattice material","authors":"Himanshu, B Pal, A Ramaswamy","doi":"10.1007/s10704-025-00882-y","DOIUrl":"10.1007/s10704-025-00882-y","url":null,"abstract":"<div><p>Architected lattice materials (ALM) have gained significant attention due to their superior mechanical properties compared to conventional bulk metals. However, limited studies in the literature focus on modeling the fracture behavior of ALM structural elements, particularly using beam kinematics coupled with phase-field (PF) damage models to reduce computational costs than analyzing an equivalent 2D model. The present study develops a beam-based PF model using Timoshenko beam theory to simulate localized damage evolution in brittle ALM grids. The proposed model employs a homogenized damage function to capture the overall damage state across the beam cross-section, bypassing the need to resolve damage variations within the section. Two damage approximation functions, constant and parabolic, are explored to describe damage across the cross-section. Damage evolution is attributed to a combination of tensile axial energy, shear energy, and a fraction of flexural strain energy. A series of numerical simulations, from isolated beam tests to full-scale ALM grid analyses, demonstrate the efficacy of the proposed model. Results indicate that the fraction of flexural strain energy(<span>(alpha )</span>) influencing damage evolution varies with the beam’s depth-to-length ratio, while boundary conditions show negligible impact on <span>(alpha )</span> for a fixed ratio. Model validation through comparisons with 2D simulations and experimental data highlights accurate predictions of load-displacement responses and crack patterns. Moreover, the proposed approach achieves significant computational efficiency, reducing the degrees of freedom for the lattice system from 3.2 million in a 2D model to just 58,000. Correspondingly, computational time decreases from 14 hours and 43 minutes to only 7 minutes and 20 seconds. These results underscore the potential of the proposed beam-based PF model as a computationally efficient and accurate tool for analyzing damage behavior in ALM.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144843324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On small scale nonlinearity and nested crack tip fields in a neo-Hookean material","authors":"Yuan Li, Brian Moran","doi":"10.1007/s10704-025-00880-0","DOIUrl":"10.1007/s10704-025-00880-0","url":null,"abstract":"<div><p>This paper investigates the stress singularity at the crack tip in a two-dimensional Neo-Hookean hyperelastic material, with a focus on how far-field strain influences the crack tip field distribution. The study demonstrates that, under small far-field strains, the crack tip field can be generally divided into three regions: Region I—the asymptotic neo-Hookean crack tip field as <span>(rrightarrow 0)</span>; Region II—a finite-radius nonlinear neo-Hookean zone; and Region III—an outer linear elastic region. Within Region III, a subregion may still obey the asymptotic linear elastic solution when the radial distance is sufficiently small. As the far-field strain increases, both the asymptotic linear subregion and the broader linear region shrink and eventually vanish, leaving only the nonlinear zones. This multiscale structure reflects the principle of small-scale nonlinearity, wherein nonlinear effects are confined to an inner core. The inner core consists of Region I, where asymptotic neo-Hookean fields dominate, and Region II, where general nonlinear effects prevail. Initially, this inner core is nested inside Region III. At sufficiently small far-field strains, Region III itself contains an inner core that follows asymptotic linear elastic crack tip fields. As loading intensifies, Regions I and II expand, and Region III—first its asymptotic core, then the broader linear zone – .- progressively diminishes, culminating in a large-scale nonlinearity regime. We also identify and quantify the characteristic length scales over which each region exists and dominates—nonlinear fields in Regions I and II and linear elastic behavior in Region III. An important point is that at the crack tip, Region I always governs the local field, although its extent may be small under small far-field strains, making it difficult to capture in computational simulations. To address this, we introduce a rescaling method to better resolve this near-tip behavior.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10704-025-00880-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fracture failure assessment of ring-stiffened titanium alloy cylinder","authors":"Junfeng Zhang, Yinghui Liu, Xiaoming Liu, Bowen Zhang","doi":"10.1007/s10704-025-00878-8","DOIUrl":"10.1007/s10704-025-00878-8","url":null,"abstract":"<div><p>This paper presents a novel failure evaluation method for fracture instability analysis of ring-stiffened titanium alloy cylinders under hydrostatic pressure. The quantification of fracture instability behavior for a titanium alloy cylinder remains unclear. In this work, we propose a post-buckling mode analysis for fracture instability, considering the relationship between plastic strain and structural deformation. Further, a novel fracture failure criterion involving material properties and structural parameters is established, bringing the proposal of a structural failure range evaluation method for titanium alloy cylinders. By incorporating the strain rate effect into the constitutive model of the two-phase <span>(alpha +beta )</span> titanium alloy Ti-6Al-4 V, we developed a dynamic finite element model for studying the fracture instability of the titanium alloy cylinder. The theoretical results and finite element simulation results are finally verified by the collapse experiment of a titanium alloy cylinder. The findings can provide a fundamental basis for designing and service safety evaluation of titanium alloy cylinders.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct tension test on large concrete specimens - Part I: Tensile strength, fracture properties and size effect","authors":"J M Chandra Kishen, Yogesh R, Parvinder Singh","doi":"10.1007/s10704-025-00872-0","DOIUrl":"10.1007/s10704-025-00872-0","url":null,"abstract":"<div><p>The tensile strength and fracture properties of concrete play a vital role in the design of large concrete structures. These properties are evaluated from indirect tests on small-sized specimens. As concrete is known to exhibit a strong size effect, it is important to evaluate these properties from large-sized specimens through a direct tension test. In this research, we perform direct tension tests on large-sized concrete specimens under displacement control. The conditions under which the specimens have to be prepared and tested, and the challenges faced are highlighted. It is seen that the tensile strength is almost half the values that are suggested in major codes of practice. Important elastic and fracture properties under direct tension, including tensile strength, fracture toughness, fracture energy, critical crack mouth opening displacement, critical crack length, and softening law parameters, which find application in non-linear finite element models, are evaluated.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct tension test of large concrete specimens - Part II: Insights into micromechanical fracture of concrete through acoustic emission and digital imaging","authors":"R. Yogesh, J. M. Chandra Kishen","doi":"10.1007/s10704-025-00873-z","DOIUrl":"10.1007/s10704-025-00873-z","url":null,"abstract":"<div><p>In the first part of the companion paper, experimental procedures for conducting direct tension tests on large concrete specimens were discussed, together with the fracture properties and size effects. In this paper, we delve into the details of micromechanisms of fracture and failure in concrete under direct tension using digital imaging and acoustic emission (AE) techniques. The surface cracking characteristics are obtained from imaging, while the evolution of microcracks in the fracture process zone (FPZ) are predicted through AE events and energy. The differences in microcrack initiation, and their coalescence to form macrocracks for different sizes of specimens are explained, and the size of the FPZ is estimated. It is concluded that in large-size specimens, the size of FPZ is relatively smaller with the formation of microcracks, their coalescence to form macrocracks, and the propagation of the final crack taking place almost simultaneously, leading to a brittle failure.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fracture characteristics of concrete under biaxial tension–tension loading revealed by a gap tensile test: a numerical study","authors":"Peizhi Huang, Longbang Qing","doi":"10.1007/s10704-025-00864-0","DOIUrl":"10.1007/s10704-025-00864-0","url":null,"abstract":"<div><p>In practical projects, concrete members are often subjected to multiple axial stress states, and the actual fracture process is more complex. This study utilizes a novel gap tensile test method and two-dimensional random circular aggregate mesoscopic numerical simulation to investigate notched concrete fracture characteristics. On the basis of Bažant's Type II size effect law (SEL) and linear elastic fracture mechanics (LEFM), fracture parameters such as fracture energy, notch tensile strength, and fracture toughness of concrete under biaxial tensile stress were obtained. The results indicate, compared with uniaxial loading, that crack–parallel tensile stress significantly affects the key fracture parameters of concrete. As the crack–parallel tensile stress increases, the peak fracture load of all the concrete samples tend to monotonically decrease. Compared with that when the normalized crack–parallel tensile stress η = 0, the peak load decreases by approximately 5, 20, and 40% when η is 0.19, 0.38, and 0.57, respectively, for different specimen dimensions. When the normalized crack–parallel stress increases to 0.57, the fracture energy, fracture toughness, and notch tensile strength decrease by approximately 30–80%. The crack–parallel tensile stress induces predamage in the weak interfacial transition zone (ITZ) of the concrete, leading to a reduction in the load-bearing capacity. Likewise, it can be expected that this degradation effect will be even more severe in low-strength concrete.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Leon Herrmann, Lars P. Mikkelsen, Brian N. Legarth, Christian F. Niordson
{"title":"Competition between Arbitrarily Oriented Tunnel Cracks and Delamination","authors":"Leon Herrmann, Lars P. Mikkelsen, Brian N. Legarth, Christian F. Niordson","doi":"10.1007/s10704-025-00870-2","DOIUrl":"10.1007/s10704-025-00870-2","url":null,"abstract":"<div><p>We propose a method for quantifying the competition between tunnel and delamination cracking in laminates. Based on the analytical relation between the compliance derivative and the energy release rate, which we refer to as the compliance method, the competition between the two damage mechanisms is investigated based on compliance maps that may be precomputed, thus providing an efficient tool for predicting damage development in laminates without ad hoc fracture simulations. Tunnel and delamination cracking in an off-axis layer, much thinner than the load-carrying layers of a laminate, are used as an example to illustrate the proposed methodology. However, the compliance method is generalizable to any parameterizable cracking mechanism. The cracks are simulated in a specialized two-dimensional off-axis finite element framework, which fully captures the three-dimensional solution. The method is validated against the energy balance method for tunneling cracks and the virtual crack closure technique for delamination cracks. The method has great potential in the context of nondestructive testing, where future damage states can be predicted from precomputed or experimentally determined compliance maps, thus reducing computational and experimental costs.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10704-025-00870-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Huai-Zhong Liu, Wan-Xi Liang, Hong-Qiang Xie, Li Zhuo, Ming-Li Xiao, Jiang-Da He
{"title":"Influence of partial separation between rock specimen and loading device on determination of Mode II fracture toughness by shear-box test","authors":"Huai-Zhong Liu, Wan-Xi Liang, Hong-Qiang Xie, Li Zhuo, Ming-Li Xiao, Jiang-Da He","doi":"10.1007/s10704-025-00876-w","DOIUrl":"10.1007/s10704-025-00876-w","url":null,"abstract":"<div><p>Shear-box loading could partially separate rock specimen and loading device to keep moment balance, but the influence of the partial separation has not been considered in determining Mode II fracture toughness. In this study, the finite element method was employed to analyze the separation states between rock specimen and loading device in the shear-box tests with various loading angles, and the influences of the separation state on the stress intensity factors and Mode II fracture toughness were investigated by recalibrating the Mode I and Mode II dimensionless shape factors. The results indicate that the separated length increases as the initial crack length or the loading angle increases. If the separation state is not considered in the mechanical analysis, the average relative errors of the resulted Mode I and Mode II stress intensity factors are about 21.66% and 11.06%, and the relative errors of the Mode II fracture toughness determined by the Mohr–Coulomb fracture criterion are greater than 9.3%. Therefore, the influence of the separation state between rock specimen and loading device cannot be ignored in the fracture analysis of the shear-box test.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Formation mechanism of two different crack surfaces in a median crack formed by scribing wheel","authors":"Kumiko Murakami, Souta Matsusaka, Sho Itoh, Hirofumi Hidai, Mitsuru Kitaichi","doi":"10.1007/s10704-025-00871-1","DOIUrl":"10.1007/s10704-025-00871-1","url":null,"abstract":"<div><p>Two types of crack appearances may be observed in a median crack formed by scribing wheels. A cracked surface with a striped pattern and smooth cracked surface are formed, and a distinct crack-arrest line is formed at the boundary between them. This study explored the mechanisms that control changes in crack surfaces. The median crack caused by wheel scribing propagated within a symmetric stress field composed of axial and shear stresses. Numerical analysis revealed that the direction of the shear stress changed in regions that formed cracks with stripe patterns and smooth cracks. Depending on the combination of the crack propagation direction and symmetry shear stress direction, the crack propagated toward or deviated from the symmetry plane. These crack-propagation characteristics caused differences in the appearance of the crack surface. The existence of an area behind the scribing wheel where the crack temporarily stopped was predicted by estimating the crack behavior based on the stress intensity factors. This temporary crack stop was the cause of the distinct crack arrest lines. This study suggests that crack propagation behavior and surface appearance of cracks can be controlled by generating a symmetrical shear stress field in an appropriate direction.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"249 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10704-025-00871-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}